Simple random walks along orbits of Anosov diffeomorphisms (Q2714698)

The authors consider a Markov process, a simple random walk along orbits of an Anosov diffeomorphism \(S\) of a smooth compact manifold \(M\). A point \(x\in M\) jumps to a point \(S(x)\) with probability \(p(x)\) and to a point \(S^{-1}(x)\) with probability \(1-p(x)\). The diffeomorphism \(S\) has an invariant (Gibbs) measure \(\mu\). If an invariance principle holds for the underlying Anosov system, the simple random walk itself has no absolutely continuous invariant measure with respect to \(\mu\).NEWLINENEWLINEFor the entire collection see [Zbl 0952.00070].